《Galois theory》 H.E. p. 59 (S44) * * * 12:29 证明的第四段。 Lemma . If U(X, r) = V(X, r)·W(X, r) where U, V, W are polynomials in two variables with coefficients in K (so that U(X, r), V(X, r), and V(X, r) are polynomials in one variable X with coefficients in K(r) = K') ...
《Galois theory》 H.E. p. 59 (S44) * * * 16:09 证明的第二段。 Since H(X) has coefficients in K' = K(r), where r is a pth root of k, and since every element of K' can be expressed as a polynomial in r with coefficients in K,... ---- 因为 H(x) 的系数在 K' = K(r) 中，其中 r ...
《Galois theory》 H.E. p. 59 (S44) * * * 16:00 第一段 Galois states in his Propositions II and III the main facts about the way in which the Galois group is reduced when the field of known quantities K is extended. ---- 伽罗瓦在他的命题 II 和 III 里陈述了关于当已知量的域 K 扩张时 ...
《Galois theory》 H.E. p. 56 (S42) * * * 12:52 2. Show that a subgroup H of a group G partitions a presentation of G into presentations of H and, in particular, that the number of elements in H divides the number of elements in G. ---- 群 G 的子群 H 分割 G 的表述为 H 的若干表述，并 ...
《Galois theory》 H.E. p. 56 (S42) * * * 14:53 2. Show that a subgroup H of a group G partitions a presentation of G into presentations of H and, in particular, that the number of elements in H divides the number of elements in G. ---- 群 G 的子群 H 分割 G 的表述为 H 的 ...
《Galois theory》 H.E. p. 56 (S42) * * * 15:23 Fifth Exercise Set 1. Show that a set of substitutions of n objects a, b, c, ... is a group if and only if it is closed under composition. ---- 置换的集合构成群当且仅当它在复合运算之下封闭。 . 证明：1) 置换的集合(记作 ...
《Galois theory》 H.E. p. 55 (S42) * * * 18:33 第四段 As a final example, consider the equation x^4 + 1 = 0 (the equation for the primitive 8th roots of unity). ---- 作为最后的例子，考虑方程x^4 + 1 = 0(本原8次单位根的方程)。 . 评论：此例是 x^p - k = 0 的特 ...
《Galois theory》 H.E. p. 55 (S42) * * * ？？？ 第三段 Another example of interest is an equation of the form x^p = k where the known quantities K include k and a primitive pth root of unity α (with p prime). ---- 另一个有用的例子是形如 x^p = k 的方程，其中已知量 K 包 ...
《Galois theory》 H.E. p. 54~55 (S42) * * * 9:14 第二段 His other example is the group of the equation x^(p-1) + x^(p-2) + ... + x + 1 = 0 satisfied by the primitive pth roots of unity where p is prime. ---- 他的另一个例子是方程x^(p-1) + x^(p-2) + ... + x + 1 = 0， ...
研究生如何自救？（上）
博文
视频
基金
相册
收藏
积分
会议